can someone explain why they continue to play after time runs out? what's this "extra time" crap?

It's actually called stoppage time. This is the time that elapses when the ball goes out of bounds or someone is down with an injury or so forth. It actually helps speed up the flow of the game instead of making sure the clock stops and restarts every time.

Did you also happen to notice that the clock counts up instead of down?

can someone explain why they continue to play after time runs out? what's this "extra time" crap?

It's called stoppage time. If you notice, the clock continues to run during injuries and out of bounds and stuff like that...stoppage time is all that time that was wasted, added on to the end. It is only decided by one referee so they can end the game whenever they want after 90:00.